572 LAND SURVEYING. 



of the various triangles, and trapezoids, and bringing out the total 

 area of t]_e whole survey, which is performed in the following 

 manner. 



1. The base and perpendicular of any triangle multiplied into 

 each other, gives twice the area of such triangle ; or, the base 

 multiplied by half the perpendicular, is equal to the area of the 

 triangle. 



2. The sum of the parallel sides of any trapezoid (i.e., a four- 

 sided figure having two of its sides parallel), multiplied by the 

 perpendicular distance between them, gives twice the area of such 

 trapezoid ; or, half the sum of the parallel sides, multiplied by the 

 perpendicular, is equal to the area of the trapezoid. 



3. The number of square links in an acre is 100,000. Hence 

 this rule : square links are reduced to acres by cutting off five 

 figures to the right, as a remainder, which is to be multiplied 

 successively by 4 for roods, 40 for poles, 30 J for yards, and 9 for 

 feet, at each multiplication cutting off 5 figures to the right ; 

 the numbers on the left of the point being acres, roods, poles, 

 yards, and feet. 



Surveys are computed in the following manner. 

 Required the area of the field A C B/ e d D ? 



Links. 



Triangle A B C = A B 900 X C E 480 =* 432000 



Triangle A B D = A B 900 X D E 510 = 459000 



Offsets. 



Triangle D a d = D a 150 X d 150 = 22500 



Trapezoid a d e b = a d 150 + b e 90 X & 270 = 64800 

 Trapezoid b efc = be 90 + cf 180 X b c 150 = 40500 



Triangle cf B = cf 180 X c B 180 = 32400_ 



according to the Rule, divide by 2)1051200 



square links 5.25600 



4 



1.02400 

 40 



".96000 

 30J 



29.04000 

 Content of the field 5 acres, 1 rood, poles, 29 yards. 



GLASGOW : 

 W. O. BLACKIE AND CO., PRINTEES, VILLATIELD. 



